A highly compact, stable mechanism for enabling a chair to perform rocking and gliding movements, and optionally swiveling movement, includes a channel-shaped frame mounting member mounted to a chair frame, and an inverted channel-shaped base mounting member mounted on a base. The mounting members are...http://www.google.com/patents/US5427433?utm_source=gb-gplus-sharePatent US5427433 - Rocking, gliding chair and mechanism

A highly compact, stable mechanism for enabling a chair to perform rocking and gliding movements, and optionally swiveling movement, includes a channel-shaped frame mounting member mounted to a chair frame, and an inverted channel-shaped base mounting member mounted on a base. The mounting members are interconnected by one pair of front and one pair of rear swing arms.

Images(6)

Claims(27)

What is claimed as new and desired to be protected by Letters Patent is set forth in the appended claims:

1. A rocking, gliding chair, comprising:

(a) a base;

(b) a body-supporting chair frame, including a seat, a backrest and armrests positioned at opposite sides of the seat; and

(c) means for mounting the seat of the chair frame on the base for rocking and gliding movement relative to the base, including

(i) a one-piece, rigid, channel-shaped base mounting member having a generally planar base plate mounted on the base, and a pair of generally planar base side walls integral with the base plate and extending in mutual parallelism upwardly from the base plate,

(ii) a one-piece, rigid, channel-shaped frame mounting member inverted relative to the base mounting member and having a generally planar top plate overlying the base plate and mounted centrally underneath and fixed to the seat forwardly of the backrest and interiorly of the armrests, and a pair of generally planar frame side walls integral with the top plate and extending in mutual parallelism downwardly from the top plate and overlapping the base side walls interiorly of the armrests, and

(iii) one pair of front and one pair of rear swing arms, each pair being located between a respective base side wall and a respective overlapping frame side wall, each arm having opposite ends respectively pivotably connected to a respective base side wall and a respective overlapping frame side wall.

2. The chair according to claim 1, wherein the base side walls extend toward, but terminate short of, the top plate; and wherein the frame side walls extend toward and past the base plate.

3. The chair according to claim 2, wherein each of the base side walls and of the frame side walls has a trapezoidal shape; and wherein each plate has a rectangular shape.

4. The chair according to claim 1, wherein each front arm has an upper end region pivotably connected to a respective base side wall at an upper front pivot, and a lower end region pivotably connected to a respective overlapping frame side wall at a lower front pivot; and wherein each rear arm has an upper end region pivotably connected to a respective base side wall at an upper rear pivot, and a lower end region pivotably connected to a respective overlapping frame side wall at a lower rear pivot; and wherein each upper front pivot is spaced along a longitudinal direction away from a respective upper rear pivot by a predetermined upper spacing; and wherein each lower front pivot is spaced along the longitudinal direction away from a respective lower rear pivot by a predetermined lower spacing; and wherein said predetermined upper spacing is greater than said predetermined lower spacing.

5. The chair according to claim 4, wherein each arm has an offset portion located between the upper and lower end regions of a respective arm and spanning the overlap between a respective base side wall and a respective overlapping frame side wall.

6. The chair according to claim 4; wherein said predetermined upper spacing is less than 18 centimeters, wherein said predetermined lower spacing is less than 14.5 centimeters, and wherein each arm has a length which is less than 10.25 centimeters.

7. The chair according to claim 1; and further comprising stop means on the mounting means, for limiting the extent of said rocking and gliding movement relative to the base.

8. The chair according to claim 7, wherein the stop means includes two pairs of front and rear abutments, each pair being spaced apart along a longitudinal direction and mounted on a respective base side wall in the path of swinging movement of the arms.

9. The chair according to claim 8, wherein each abutment is a cushioned stop pin.

10. The chair according to claim 1; and further comprising swivel means between the base and the mounting means, for swiveling the chair frame about a vertical axis.

11. The chair according to claim 10, wherein the swivel means includes a first race formed in the base plate, a second race formed in the base, and ball bearings in the races.

12. The chair according to claim 1, wherein the seat, backrest and armrests are a unitary upholstered structure.

13. A mechanism for mounting a seat of a body-supporting chair frame having a backrest and armrests positioned at opposite sides of the seat on a base for rocking and gliding movement relative to the base, said mechanism including:

(a) a one-piece, rigid, channel-shaped base mounting member having a generally planar base plate mounted on the base, and a pair of generally planar base side walls integral with the base plate and extending in mutual parallelism upwardly from the base plate;

(b) a one-piece, rigid, channel-shaped frame mounting member inverted relative to the base mounting member and having a generally planar top plate overlying the base plate and mounted centrally underneath and fixed to the seat forwardly of the backrest and interiorly of the armrests, and a pair of generally planar frame side walls integral with the top plate and extending in mutual parallelism downwardly from the top plate and overlapping the base side walls interiorly of the armrests; and

(c) one pair of front and one pair of rear swing arms, each pair being located between a respective base side wall and a respective overlapping frame side wall, each arm having opposite ends respectively pivotably connected to a respective base side wall and a respective overlapping frame side wall.

14. The mechanism according to claim 13, wherein the base side walls extend toward, but terminate short of, the top plate; and wherein the frame side walls extend toward and past the base plate.

15. The mechanism according to claim 14, wherein each of the base side walls and of the frame side walls has a trapezoidal shape; and wherein each plate has a rectangular shape.

16. The mechanism according to claim 13, wherein each front arm has an upper end region pivotably connected to a respective base side wall at an upper front pivot, and a lower end region pivotably connected to a respective overlapping frame side wall at a lower front pivot; and wherein each rear arm has an upper end region pivotably connected to a respective base side wall at an upper rear pivot, and a lower end region pivotably connected to a respective overlapping frame side wall at a lower rear pivot; and wherein each upper front pivot is spaced along a longitudinal direction away from a respective upper rear pivot by a predetermined upper spacing; and wherein each lower front pivot is spaced along the longitudinal direction away from a respective lower rear pivot by a predetermined lower spacing; and wherein said predetermined upper spacing is greater than said predetermined lower spacing.

17. The mechanism according to claim 16, wherein each arm has an offset portion located between the upper and lower end regions of a respective arm and spanning the overlap between a respective base side wall and a respective overlapping frame side wall.

18. The mechanism according to claim 17, wherein said predetermined upper spacing is less than 18 centimeters, wherein said predetermined lower spacing is less than 14.5 centimeters, and wherein each arm has a length which is less than 10.25 centimeters.

19. The mechanism according to claim 13; and further comprising stop means on the mounting means, for limiting the extent of said rocking and gliding movement relative to the base.

20. The mechanism according to claim 19, wherein the stop means includes two pairs of front and rear abutments, each pair being spaced part along a longitudinal direction and mounted on a respective base side wall in the path of swinging movement of the arms.

21. The mechanism according to claim 20, wherein each abutment is a cushioned stop pin.

22. The mechanism according to claim 15; and further comprising swivel means between the base and the mounting means, for swiveling the chair frame about a vertical axis.

23. The mechanism according to claim 24, wherein the swivel means includes a first race formed on the base plate, a second race formed in the base, and ball bearings in the races.

24. A mechanism for mounting a seat of a body-supporting chair frame having a backrest and armrests positioned at opposite sides of the seat on a base for rocking and gliding movement relative to the base, said mechanism including:

(a) a one-piece, rigid, base mounting member mounted on the base;

(b) a one-piece, rigid, frame mounting member mounted centrally underneath and fixed to the seat forwardly of the backrest and interiorly of the armrests; and

(c) one pair of front and one pair of rear swing arms, each arm having opposite ends respectively pivotably connected to the base mounting member and the frame mounting member,

(i) each front arm having an upper and region pivotably connected to the base mounting member at an upper front pivot, and a lower end region pivotably connected to the frame mounting member at a lower front pivot,

(ii) each rear arm having an upper end region pivotably connected to the base mounting member at an upper rear pivot, and a lower end region pivotably connected to the frame mounting member at a lower rear pivot,

(iii) each upper front pivot being spaced along a longitudinal direction away from a respective upper rear pivot by a predetermined upper spacing less than 18 centimeters, and

(iv) each lower front pivot being spaced along the longitudinal direction away from a respective lower rear pivot by a predetermined lower spacing less than 14.5 centimeters.

25. The mechanism according to claim 24, wherein each arm has a length less than 10.25 centimeters.

26. The mechanism according to claim 24, wherein the mounting members are channel-shaped and inverted relative to each other.

27. A rocking, gliding, reclining chair, comprising:

(a) a base;

(b) a body-supporting chair frame, including a seat, a backrest, armrests positioned at opposite sides of the seat, and a footrest;

(c) a recliner linkage for reclining the frame to a reclined position relative to the base;

(d) means for mounting the linkage on the base for rocking and gliding movement relative to the base, including

(i) a one-piece, rigid, channel-shaped base mounting member having a generally planar base plate mounted on the base, and a pair of generally planar base side walls integral with the base plate and extending in mutual parallelism upwardly from the base plate,

(ii) a one-piece, rigid, channel-shaped frame mounting member inverted relative to the base mounting member and having a generally planar top plate overlying the base plate and mounted centrally underneath and fixed to the linkage forwardly of the backrest and interiorly of the armrests, and a pair of generally planar frame side walls integral with the top plate and extending in mutual parallelism downwardly from the top plate and overlapping the base side walls interiorly of the armrests, and

(iii) one pair of front and one pair of rear swing arms, each pair being located between a respective base side wall and a respective overlapping frame side wall, each arm having opposite ends respectively pivotably connected to a respective base side wall and a respective overlapping frame side wall; and

(e) blocking means operatively connected between the recliner linkage and the mounting means for preventing the rocking and gliding movement when the frame is in the reclined position.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention generally relates to a chair having a rocking and gliding motion and, more particularly, to a highly compact mechanism that provides a highly stable rocking and gliding action without sacrificing stability or low seat styling.

2. Description of the Related Art

Rockers and gliders are well known. For example, U.S. Pat. Nos. 4,536,029 and 4,544,201 each discloses a combined rocking, gliding chair in which a chair structure including a seat, armrests, and a backrest is suspended from multiple swing arms of a linkage mechanism that, in turn, is mounted on a stationary base. Although generally satisfactory for their intended purpose, the suspension-type chairs of the above-identified patents have not proven to be altogether desirable.

For example, the known linkage mechanism requires a clear mounting height of 18 through 25 centimeters under the seat. This is simply too high for many, modern, low seat styled, chairs, and especially for chairs having internal seat springs.

Also, the chair structure is mounted on the very bottom of the known linkage mechanism, as close to the floor as possible, in an effort to increase chair stability. However, this causes the tilt angles that the chair structure assumes, especially in its end-limiting positions, to be somewhat excessive for the comfort of a seated occupant.

In addition, the chair structure is mounted exteriorly outboard of the known linkage mechanism, as far apart as possible, in another effort to increase chair stability. However, this causes the known linkage mechanism to be somewhat wider than it otherwise had to be and, in turn, contributed to an increase in the weight and size of the overall chair.

Still another undesirable aspect related to the use of cross-stabilizer bars between front and rear pairs of swing arms on the known linkage mechanism. Such bars added complexity and cost.

SUMMARY OF THE INVENTIONObjects of the Invention

It is a general object of this invention to provide an improved rocking, gliding chair designed to meet low seat styling requirements.

Another object of this invention is to provide such a chair having a stable, comfortable, rocking and gliding motion.

An additional object of this invention is to provide a highly compact, rocking, gliding mechanism that accommodates seat springs.

Another object of this invention is to provide such a highly compact mechanism that does not require cross-stabilizer bars.

An additional object of this invention to provide such a mechanism that is easily modified to perform a swivel action during use.

Yet another object of this invention is to provide an inexpensive, stable, functional rocker and glider.

Features of the Invention

In keeping with these objects and others which will become apparent hereinafter, one feature of this invention resides, briefly stated, in a rocking, gliding chair, which comprises a base, a body-supporting chair frame, and means for mounting the chair frame on the base for rocking and gliding movement relative to the base.

In accordance with this invention, the mounting means includes a channel-shaped base mounting member having a generally planar base plate mounted on the base, and a pair of generally planar base side walls extending upwardly from the base plate. A channel-shaped frame mounting member is inverted relative to the base mounting member and has a generally planar top plate overlying the base plate and mounted to the frame, and a pair of generally planar frame side walls extending downwardly from the top plate and overlapping the base side walls. One pair of front and one pair of rear swing arms are provided. Each pair is located between a respective base side wall and a respective overlapping frame side wall. Each arm has opposite ends respectively pivotably connected to a respective base side wall and a respective overlapping frame side wall.

In the preferred embodiment, the base side walls are mutually parallel and extend toward, but terminate short of, the top plate. The frame side walls are mutually parallel and extend toward and past the base plate. Preferably each base side wall and frame side wall has a trapezoidal shape, and each plate has a rectangular shape.

Each front arm has an upper end region pivotably connected to a respective base side wall at an upper front pivot, and a lower end region pivotably connected to a respective overlapping frame side wall at a lower front pivot. Each rear arm has an upper end region pivotably connected to a respective base side wall at an upper rear pivot, and a lower end region pivotably connected to a respective overlapping frame side wall at a lower rear pivot. Each upper front pivot is spaced along a longitudinal direction away from a respective upper rear pivot by a predetermined upper spacing, preferably less than 18 centimeters. Each lower front pivot is spaced along the longitudinal direction away from a respective lower rear pivot by a predetermined lower spacing, preferably less than 14.5 centimeters. The predetermined upper spacing is always greater than said predetermined lower spacing in order to achieve the aforementioned rocking, gliding action.

Each swing arm preferably has a length which is less than 0.25 centimeters. Each arm has an offset portion located between the upper and lower end regions thereof, and spans the overlap between a respective base side wall and a respective overlapping frame side wall.

The mounting means or mechanism of this invention requires a clear mounting height between the base and top plates of less than 10.25 centimeters, much reduced compared to the 18 centimeter through 25 centimeter mounting height required in prior art constructions. This vertically compact design is ideal for modern, low seat styled chairs, and easily accommodates internal seat springs.

The body-supporting chair frame is no longer mounted on the very bottom of the mechanism as close to the floor as possible, or exteriorly outboard of the mechanism as far apart as possible, but, instead, is mounted directly on top of the top plate of the mechanism. Good chair stability is achieved, because the mechanism is so vertically compact, and the lengths of the swing arms are not overly long.

Cross-stabilizing bars are no longer needed between the front swing arms, or between the rear swing arms. When the channel-shaped frame mounting member moves back and forth, the swing arms mounted thereon move in synchronism. Moreover, the overlapping frame and base side walls effectively protect the swing arms from lateral encroachment.

Still another feature of this invention resides in providing stop means on the mechanism, for limiting the extent of the rocking and gliding movement relative to the base. Preferably, the stop means includes one pair of front and one pair of rear abutments, e.g., cushioned stop pins, each pair being spaced apart along a longitudinal direction and mounted on a respective base side wall in the path of swinging movement of the arms.

In accordance with another feature of this invention, swivel means may be provided between the base and the mechanism, for swiveling the chair frame about a vertical axis. The swivel means includes a first race formed in the base plate, a second race formed in the base, and ball bearings in the races.

The frame itself conventionally includes a seat, a backrest and a pair of armrests fixed to opposite sides of the seat. The mechanism is located underneath the seat, forwardly of the backrest, and between the armrests. The seat, backrest and armrests may be a unitary upholstered structure, or in the case of a recliner, the backrest is movable relative to the seat. In order to prevent the rocking, gliding motion when the recliner is in a reclined position, a blocking linkage means is incorporated with the mechanism.

The novel features which are considered as characteristic of the invention are set forth in particular in the appended claims. The invention itself, however, both as to its construction and its method of operation, together with additional objects and advantages thereof, will be best understood from the following description of specific embodiments when read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a broken-away perspective view of a rocking, gliding chair equipped with a mechanism in accordance with this invention;

FIG. 2 is an enlarged perspective view of the mechanism used in the chair of FIG. 1;

FIG. 3 is a broken-away view of the chair of FIG. 1 in a rear, end-limiting tilted position;

FIG. 4 is a view analogous to FIG. 3, but showing the chair in a forward, end-limiting position;

FIG. 5 is a broken-away sectional view taken along the line 5--5 of FIG. 3;

FIG. 6 is a sectional view of a reclining chair equipped with a modified mechanism in accordance with this invention;

FIG. 7A is an enlarged sectional view of a modified mechanism for use in the chair of FIG. 6 in a neutral position;

FIG. 7B is a view analogous to FIG. 7A, but in a "rocked forward" position;

FIG. 7C is a view analogous to FIG. 7A, but in a "rocked rearward" position; and

FIG. 7D is a view analogous to FIG. 7A, but in a "blocked" position.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to FIG. 1 of the drawings, reference numeral 10 generally identifies a rocking, gliding chair having a stationary base 12, a body-supporting chair frame 14, and a mechanism 20 (shown in isolation in FIG. 2) for mounting the chair frame 14 on the base 12 for rocking and gliding movement relative to the base 12. Base 12 is illustrated as a circular platform, but other types of base structures can be used, such as multiple spider legs radiating outwardly from a central axis. Frame 14 includes a seat 16, a backrest 18, and a pair of armrests 22 which, in FIG. 1, are united together as one unitary structure of conventional construction, including upholstered wooden frame parts. The chair has a relatively low seat, which means that the seat 16 is positioned above the floor within a certain minimum range. Seat 16 may include a T-cushion, wherein the front ends of the cushion are, as illustrated, positioned beyond the armrests 22.

Referring now to FIG. 2, the mechanism 20 includes a channel-shaped base mounting member 24 having a generally planar base plate 26 mounted on the base 12. Non-illustrated threaded fasteners passing through mounting holes 30 could be used for a fixed mounting or, as described below, a swivel mounting could be used. Base plate 26 has a rectangular shape, and a mounting hole 30 is located at each corner. A pair of generally planar base side walls 32, 34 extend upwardly in mutually parallelism from the base plate 26. Each base side wall has a generally trapezoidal shape. Member 24 is made of a rigid metal.

Mechanism 20 further includes a channel-shaped frame mounting member 36 inverted in a mirror-symmetrical relationship with the base mounting member 24. Frame mounting member 36 has a generally planar top plate 38 mounted to the frame 14 with the aid of threaded fasteners 40 (see FIG. 5) passing through mounting holes 42. Top plate 38 has a generally rectangular shape, and a mounting hole 42 is located at each corner. A pair of generally planar frame side walls 44, 46 extend downwardly in mutually parallelism from the top plate, and exteriorly overlap the base side walls 32, 34, respectively. Each frame side wall 44, 46 has a generally trapezoidal shape. Member 46 is also made of a rigid metal.

A front swing arm 50 has an upper end region 52 pivotably connected to a base side wall 32 at an upper front pivot 54; a lower end region 56 pivotably connected to frame side wall 44 at a lower front pivot 60; and an offset portion 62 spanning the distance between the overlapping base and frame side walls 32, 44.

A rear swing arm 64 has an upper end region 66 pivotably connected to base side wall 32 at an upper rear pivot 68; a lower end region 70 pivotably connected to frame side wall 44 at a lower rear pivot 72; and an offset portion 74 spanning the distance between the overlapping base and frame side walls 32, 44.

Another front swing arm 76 has an upper end region 78 pivotably connected to base side wall 34 at an upper front pivot 80; a lower end region 82 pivotably connected to frame side wall 46 at a lower front pivot 84; and an offset portion 86 spanning the distance between the overlapping base and frame side walls 34, 46.

Another rear swing link 88 has an upper end region 90 pivotably connected to base side wall 34 at an upper rear pivot 92; a lower end region 94 pivotably connected to frame side wall 46 at a lower rear pivot 96; and an offset portion 98 spanning the distance between the overlapping base and frame side walls 34, 46.

All of the arms are links stamped from rigid metal. Each arm has a length which, in the preferred embodiment, is less than 10.25 centimeters. Each end region of the arms constitutes a large bearing surface area, thereby enhancing resistance to side sway. The longitudinal distance between the front and rear upper pivots 54, 68 and 80, 92, also known as the predetermined upper spacing, is less than 18 centimeters. The longitudinal distance between the front and rear lower pivots 60, 72 and 84, 96, also known as the predetermined lower spacing, is less than 14.5 centimeters. The upper spacing is always greater than the lower spacing in order to achieve the gliding action.

In operation, a seated occupant shifts his or her weight to move the chair between the rearward and forward tilted positions of FIGS. 3 and 4. The end-limiting positions are defined by the stop pins 100, 102. The angle "A" in FIG. 3 is defined as the angle included between each front swing arm and a line extending through the respective upper front and rear pivots of the front and rear arms. This angle "A" can be anywhere in a range of 21° through 130° and the chair will still exhibit great stability.

It will further be noted from FIGS. 3 and 4 that the swing arms are virtually always covered by the side walls of the frame and base members, thereby providing lateral protection of the swing arms. Also, there are no cross-stabilizer bars between the front swing arms, or between the rear swing arms. The channel-shaped frame and base mounting members provide for a high degree of resistance to side sway. It is also noted that the seat, more precisely the wooden frame elements of the seat, are directly mounted on top of the top plate of the frame mounting member, thereby ensuring a simple, rapid assembly, and without sacrificing chair stability.

The mechanism herein can also provide for a swivel motion about a vertical axis. For this purpose, the underside of the base plate 26 is formed with a circular race 104, and the upper side of the base is formed with a corresponding circular race 106. A plurality of ball bearings 108 is mounted in both races. Thus, for very little additional expense, a rocking, gliding chair can also be equipped with a swivel motion.

As shown in FIG. 6, the invention may be incorporated in chairs where the backrest is movable relative to the seat, or in other action chairs, such as reclining chairs. Thus, as shown in FIG. 6, a reclining chair 110 of conventional construction may be equipped with the mechanism 20 of this invention. The mechanism 20 is in this case, conveniently mounted to a pair of fore and aft, metal tubes 112, 114 of rectangular cross-section. The tubes extend transversely underneath the seat between the armrests. In order to prevent mechanical interference with the various links of the recliner, the shapes of the side walls of the base and frame mounting members may be modified, as shown. However, the basic structure of the mechanism remains the same. The ratio of the lengths of the swing arms relative to the upper spacing and lower spacing lengths remains the same.

Recliner 110 includes a footrest 116 and a footrest linkage 118. As best shown in FIGS. 7A-7D, a blocking linkage is installed to prevent the rocking and gliding movement of the chair recliner in one of its reclined positions.

Thus, the blocking linkage includes an angled blocking link 120 having an end region 126 pivotably connected to a bracket 123 fixed to, and extending downwardly from, the top plate 38 centrally of the mechanism 20. An opposite end region 128 of the blocking link 120 is pivotably connected to the recliner linkage of the chair. A central region of the blocking link 120 is pivotably connected at pivot 130 to one end of a first, linear link 122 whose opposite end is pivotably connected at pivot 132 to one end of a second, linear link 121 whose opposite end is pivotably connected at pivot 134 to a bracket 124 fixed to, and extending upwardly from, the base plate 26 rearwardly within the mechanism and in vertical alignment with the bracket 123. A blocking pin 125 is fixed to the blocking link 120 between its end region 128 and its central region, and in vertically overlying relationship with the first link 122.

The blocking link 120 is normally constrained by the recliner linkage connected at end region 128, and links 121 and 122 are free to move between the "rocked forward" position of FIG. 7B and the "rocked rearward" position of FIG. 7C. In other words, the recliner, when it has not been moved to any reclining position, is free to perform rocking, gliding movement. However, once the recliner is moved to a reclined position, its recliner linkage forces the blocking link 120 from its neutral position, (shown by phantom lines in FIG. 7D) downwardly in the direction of the arrow B. During this downward movement, blocking pin 125 engages link 122 and pushes link 122 into alignment with link 121. The "on center" alignment between links 121, 122 prevents to-and-fro motion, thereby blocking any rocking, gliding motion in the selected reclined position. Once the recliner is moved back to its neutral position, the blocking link 120 is lifted back to its position in FIG. 7A and, as before, the chair is free to move to-and-fro between the positions of FIGS. 7B and 7C.

It will be understood that each of the elements described above, or two or more together, also may find a useful application in other types of constructions differing from the types described above.

While the invention has been illustrated and described as embodied in a rocking, gliding chair and mechanism, it is not intended to be limited to the details shown, since various modifications and structural changes may be made without departing in any way from the spirit of the present invention.

Without further analysis, the foregoing will so fully reveal the gist of the present invention that others can, by applying current knowledge, readily adapt it for various applications without omitting features that, from the standpoint of prior art, fairly constitute essential characteristics of the generic or specific aspects of this invention and, therefore, such adaptations should and are intended to be comprehended within the meaning and range of equivalence of the following claims.